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Facebook's growth is slowing down and its profit shrank in the last quarter. If it goes public May 18th at $35 a share -- a $96 billion valuation -- and then pops to $75 on the first day, that will put the social network's market capitalization at $206 billion. And unless it can accelerate growth -- possibly by grabbing a share of the mobile advertising market -- that 206 Price/Earnings ratio is sending a powerful message: Do Not Buy This Stock!

During its IPO road show, investors have been asking Facebook executives about its mobile strategy. According to the Washington Post, Facebook plans to follow its users from the desktop to the "mobile Web and apps," and its advertising revenues will migrate accordingly.

Facebook is targeting those mobile users through so-called “sponsored stories” in posts that come from companies to advertise their products. Simply put, Facebook is selling companies a chance to deliver mobile infomercials to Facebook users.

Inside Facebook reports that Facebook is administering customer surveys on their Facebook apps asking how’d they would like to see advertisements on Facebook's mobile site. Specifically, users look at two ads "from different companies or in different formats and [are] asked which they prefer. Users are given three choices: neither, top ad or bottom ad.”

In this way, Facebook can find out if users like ads "with pictures, surveys or other elements as well as what kinds of ads they like to see," according to Inside Facebook. As I posted April 24th, my informal survey of 80 Babson College students suggests that any increase in advertising will drive them away from Facebook.

But if Facebook can make the ads sufficiently inoffensive that it will not lose its coveted audience, it could generate $2.7 billion in mobile advertising revenue by 2016. After all, Facebook got 78 million unique mobile visitors in March 2012 -- with 80% of user's time spent on apps and the other 20% via browser, according to comScore (SCOR).

And Facebook has an estimated 25% to 30% of the U.S. display advertising market, according to Flurry Analytics. Meanwhile, eMarketer estimates mobile advertising spending in the US will grow 80% to $2.61 billion by the end of 2012 and hit $10.8 billion by 2016.

If Facebook snared 25% of the mobile advertising market by 2016, that would add about $2.7 billion to its revenue and -- applying its first quarter 2012 net margin of 20% -- would represent an additional $540 million in profit by 2016.

Capstone Investments expects Facebook's annual revenue growth rate to slow to 32% and its margins to decline 5 percentage points by 2016. Applying these assumptions to Facebook's 2011 revenues of $3.71 billion yields a 2016 revenue estimate of $14.1 billion and net income of $2.12 billion (assuming a net margin of 15% thanks in part to a decline in premium ad revenues).

If we assume that Capstone did not figure in mobile advertising profits, the $540 million estimated above would boost 2016 profits by 25% to $2.66 billion. Given the reluctance of Facebook users to put up with ads, I'd guess that this estimate is too high.

But even if that guess proves right, it means that Facebook's net income will increase at a 21.6% annual rate by 2016 and that's nowhere near fast enough to justify Facebook's P/E of 206 at the end of its first day of trading next week. After all, Apple (AAPL) is growing its profit at 85% and trades at a P/E of almost 14.